Answer:
The tangent plane equation for the hyperboloid
.
Step-by-step explanation:
We have
The ellipsoid's equation is
The equation for the tangent plane at the point 
(Given)
The hyperboloid's equation is
F(x,y,z)=
The tangent plane equation at point
The tangent plane equation for the hyperboloid is
The tangent plane equation
Hence, the required tangent plane equation for the hyperboloid is
The diagrams for parts A and C are included here. For part B, we have circle O. We begin by drawing two radii OA and OC, connecting points A and C to create chord AC. The radius intersects chord AC at point B, bisecting AC into equal segments AB and BC. This gives us two triangles, ΔOBA and ΔOBC, where OA equals OC (since they're radii), OB equals OB (by the reflexive property), and AB is equal to BC (as stated in the question). By applying the SSS triangle congruence criterion, we conclude that ΔOBA is congruent to ΔOBC, allowing us to deduce that ∡OBA equals ∡OBC, both measuring 90°. Thus, OB is perpendicular to AC. Moving on to part D, we again work with circle O and draw the two radii OA and OC, joining points A and C to create chord AC. The radius intersects AC at point B, where AB is perpendicular to AC, meaning ∡B equals 90°. We then consider the right triangles ΔOBA and ΔOBC, and given OA equals OC (the radii), and OB equals OB (reflexive property), we conclude through the HL triangle congruence that ΔOBA is congruent to ΔOBC. Consequently, we find BA equal to BC, thus OB bisects AC.
Response: a) 0.9980, b) 0.0013, c) 0.0020, d) 0.00000026, e) 0.0318
Detailed explanation:
In Problem 8-4, the computer time-sharing system experiences teleport inquiries at an average rate of 0.1 per millisecond. We are tasked with determining the probabilities of the inquiries over a specific period of 50 milliseconds:
Given that
Applying the Poisson process, we find that
(a) at most 12
probability= 
(b) exactly 13
probability=
(c) more than 12
probability=
(d) exactly 20
probability=
(e) within the range of 10 to 15, inclusive
probability=
Thus, a) 0.9980, b) 0.0013, c) 0.0020, d) 0.00000026, e) 0.0318
Answer:
a) The outlier is the point located at the bottom right of the graph
b) The plotted points resemble a line that has a positive gradient
c) By conducting correlation analysis, we can determine the strength of the correlation
Step-by-step explanation:
a) The problem presents a scenario where Igor, who has recently moved, is experienced but needs to retrain medically to practice in the UK
Thus, he corresponds to the outlier situated nearest to the graph's bottom right
b) According to the scatter graph, there's a direct relationship showing that as a doctor's age increases, their annual salary tends to climb as well
Referencing the graph:
Age Salary
22 £28000
26 £30000
34 £44000
38 £42000
42 £30000
42 £46000
50 £55000
The data points follow a line demonstrating the proportional increase of salary with age.
c) To reinforce this conclusion's reliability, correlation analysis should be conducted to ascertain the relationship between age and annual incomes.
Answer:
86/105
Step-by-step explanation:
May possesses 4/15 meters of lace
Lovie has lace that exceeds May's by 2/7 meters
4/15 + 2/7
= 58/105
Consequently, the total amount of lace they have is calculated as
= 4/15 + 58/105
= 86/105
Thus, together they own 86/105 meters of lace
